SOLUTIONS AND ANALYSES OF FRACTIONAL-TALBOT ARRAY ILLUMINATIONS

Gratings with different opening ratios (1/M) will have different fract ional-Talbot distances with pure-phase distributions. We describe a si mple step-by-step numerical method, which call be used to calculate th e positions of the fractional-Talbot pure-phase distributions and thei r corresponding phases. It is observed that the pure-phase distributio ns will only be at p(1/2M)Z(T) distances (where Z(T) is the Talbot dis tance, p and M are integers and have no common divisor), and that thef t: are specific symmetries of the phase distributions at the different fractional-Talbot distances. It is also found that the neighbouring-p hase differences of the pure-phase distributions me regularly rearrang ed. depending on the different fractional-Talbot distances. So we can obtain thr pure-phase distributions from the regularly-rearranged neig hbouring-phase-difference distributions at the different fractional-Ta lbot distances, without using a step-by-step numerical method. (C) 199 8 Elsevier Science B.V.